378 Professor Sir James Dewar [Jan. 18, 



However, it soon coalesced with the Hquid sarface, forming a half 

 dodecahedron in the centre surrounded by a symmetrical ring of six 

 half bubbles all resting on the liquid, and three whole bubbles 

 superposed regularly above these, each of the nine external bubbles 

 springing from one facet of the central "cell." The completed 

 structure, of which this was the half, would thus have consisted of 

 twelve pentagonal pyramidal frustums round a dodecahedron, the 

 bases of the pyramids being the outer curved bubble surfaces. Such 

 a complex was obtained separately, but it is diffcult to show the 

 configuration by means of a photograph. 



Symmetrical Clusters of Bubbles. 



Equal-sized bubbles are readily built up into well-defined groups 

 that have many interesting properties. Their spherical contours, 

 interlaced by a network of reflecting films, give them a graceful 

 symmetry. Up to an aggregate of eight the growth is fairly simple. 

 Each successive bubble springs instantaneously into its place with 

 the appearance of being partly absorbed, though of course retaining 

 its volume practically unchanged. Two bubbles thus coalesce into 

 two spherical segments joined by a circular plane film. When a 

 third bubble is introduced between these two the spherical boundaries 

 are further reduced, and are spaced out between three equally in- 

 clined plane films, which ai'e segments of circles in contact round 

 the axis of symmetry. 



With four bubbles there are two possible arrangements ; the 

 more stable form has the fourth bubble resting symmetrically on the 

 group of three, so that the four segments are equally spaced on the 

 frame of a regular tetrahedron. Six plane films in the shape of 

 circle sectors are thus produced by the four segments coalescing 

 round the centroid of the tetrahedron (Eig. 18a). But if the fourth 

 bubble be introduced between any two of the three-group instead of 

 at the junction of all three, then the form shown in Fig. 18^ is 

 obtained, which has a central plane film shaped like a rectangle with 

 its short sides slightly curved, and two pairs of equally incHned 

 planes springing from its long sides. These five planes constitute a 

 frame linking the four bubble segments together. 



In Fig. 19 these frames outlined in wire are shown as they appear 

 {a) for the group of three ; and (&), (c) for the two forms of the 

 group of four ; while Fig. 20 (outer set) gives the sections through 

 the groups to show the inclination between the plane films, and the 

 trace of the outer contours. 



Only one arrangement of the five-group has been obtained. It 

 is formed when two additional segments interpenetrate, one at each 

 end of the axis of the three-group, the three upper plane films 

 thus formed, meeting in one point of this axis, and the three lower 

 plane films meeting in another point of the same axis. 



